1. Simplify $\sqrt[3]{448b^{3}h^{2}}$. - Factor $448 = 64 \times 7$. - Cube root of $b^{3}$ is $b$. - Cube root of $448b^{3}h^{2} = \sqrt[3]{64 \times 7 \times b^{3} \times h^{2}}$. - Cube root of $64$ is $4$, so the expression is $4b\sqrt[3]{7h^{2}}$. 2. Simplify $\sqrt{12p}$. - Factor $12 = 4 \times 3$. - $\sqrt{12p} = \sqrt{4 \times 3p} = \sqrt{4} \times \sqrt{3p} = 2\sqrt{3p}$. 3. Simplify $\sqrt{36z^{2}}$. - $\sqrt{36z^{2}} = \sqrt{36} \times \sqrt{z^{2}} = 6 \times |z|$ (absolute value for square root of squares). 4. Simplify $\sqrt{8}$. - Factor $8 = 4 \times 2$. - $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$. 5. Simplify $\sqrt[3]{8}$. - Cube root of $8$ is $2$. 6. Simplify $\sqrt{64}$. - Square root of $64$ is $8$. 7. Simplify $\sqrt[3]{64z^{3}}$. - Cube root of $64$ is $4$. - Cube root of $z^{3}$ is $z$. - So the full simplification is $4z$. 8. Simplify $\sqrt{112}$. - Factor $112 = 16 \times 7$. - $\sqrt{112} = \sqrt{16 \times 7} = 4\sqrt{7}$. 9. Simplify $\sqrt[3]{275b^{3}h^{2}}$. - Factor $275 = 25 \times 11$. - Cube root of $b^{3}$ is $b$. - Cube root of $275b^{3}h^{2} = \sqrt[3]{25 \times 11 \times b^{3} \times h^{2}}$. - There is no perfect cube in 25 or 11, so it equals $b\sqrt[3]{275h^{2}}$. 10. Simplify $\sqrt[3]{135 y p^{2}}$. - Factor $135 = 27 \times 5$. - Cube root of 27 is 3. - There are no cube powers of $y$ or $p^{2}$. - So expression is $3 \sqrt[3]{5 y p^{2}}$. Final answers: 1) $4b\sqrt[3]{7h^{2}}$ 2) $2\sqrt{3p}$ 3) $6|z|$ 4) $2\sqrt{2}$ 5) $2$ 6) $8$ 7) $4z$ 8) $4\sqrt{7}$ 9) $b\sqrt[3]{275h^{2}}$ 10) $3\sqrt[3]{5 y p^{2}}$